Real Madrid had an option to re-buy the player for €12 million during the next two seasons; however, after Fábio Coentrão's transfer to the Spanish club, both parties agreed to cancel the buyback clause.

[26] He scored his first La Liga goal on 22 September, netting the last of a 3–0 away win over Getafe CF through a penalty, but was later sent off;[27] he was dismissed the following 30 May for striking Rayo Vallecano's Toño, and banned for three games by the Royal Spanish Football Federation.

[29][30] After moderate returns in his first three seasons at the Mestalla Stadium, he scored a career-best 16 goals (19 in all competitions) in 2017–18 as the Marcelino García Toral-led team qualified for the group stage of the UEFA Champions League;[31] in late November 2017, he was rewarded with a new deal through 2022 with a reported release clause of €120 million.

[32] On 29 January 2019, Rodrigo scored a second-half hat-trick – including two goals in injury time – as the hosts defeated Getafe 3–1 in the quarter-finals of the Copa del Rey, winning the tie 3–2 on aggregate.

[34] On 17 September 2019, Rodrigo scored the only goal of the match in the first Champions League group stage fixture, providing Valencia's first ever win against Chelsea in the club's history.

[43] Having missed several games through a groin injury at the beginning of 2021,[44] he was used sparingly by Marcelo Bielsa upon his return before hitting strong form at the end of the campaign, scoring his first brace for the club on 15 May in a 4–0 away victory over Burnley.

[48] On 28 January 2023, Rodrigo sustained a bone and ligament injury during a 3–1 win at Accrington Stanley in the fourth round of the FA Cup,[49] and was sidelined until his return as a 66th-minute replacement for Patrick Bamford in the 2–2 home draw with Brighton on 11 March.

[50][51] He went on to manage three more league goals for the remainder of the season, being Leeds' top scorer, but was stricken with injury again – plantar fasciitis – against West Ham, scoring in the 3–1 loss at London Stadium.

[52] On 13 July 2023, Qatar Stars League club Al-Rayyan SC triggered a relegation release clause inserted into Rodrigo's Leeds contract, signing the player.

On 3 October 2014, he was one of 23 players selected by Vicente del Bosque for UEFA Euro 2016 qualifying matches against Slovakia and Luxembourg,[57] making his debut in the latter game by replacing Diego Costa in the 82nd minute and assisting the fourth and last goal for Juan Bernat.

[58] On 6 October 2017, nearly three years after his first cap, Rodrigo marked his second by starting and scoring the first goal in a 3–0 home defeat of Albania in the 2018 FIFA World Cup qualifiers, in Alicante.

He is a lifelong friend of the latter's sons Thiago Alcântara and Rafinha, who were raised in footballing terms at FC Barcelona and also represented Spain and Brazil respectively, and was erroneously reported to be their cousin.